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National and Regional Contests
Switzerland Contests
Switzerland - Final Round
2022 Switzerland - Final Round
3
3
Part of
2022 Switzerland - Final Round
Problems
(1)
f(f(m)f(n)) = mn, f(2022a + 1) = 2022a + 1
Source: Switzerland - 2022 Swiss Final Round p3
11/17/2022
Let
N
N
N
be the set of positive integers. Find all functions
f
:
N
→
N
f : N \to N
f
:
N
→
N
such that both
∙
\bullet
∙
f
(
f
(
m
)
f
(
n
)
)
=
m
n
f(f(m)f(n)) = mn
f
(
f
(
m
)
f
(
n
))
=
mn
∙
\bullet
∙
f
(
2022
a
+
1
)
=
2022
a
+
1
f(2022a + 1) = 2022a + 1
f
(
2022
a
+
1
)
=
2022
a
+
1
hold for all positive integers
m
,
n
m, n
m
,
n
and
a
a
a
.
algebra
functional equation
functional